Strictly Proper Decision Markets A reminder about Problem set 2 Due - - PowerPoint PPT Presentation

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Strictly Proper Decision Markets A reminder about Problem set 2 Due - - PowerPoint PPT Presentation

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Strictly Proper Decision Markets A reminder about Problem set 2 Due in 8 days Project proposals are due less than a week after Literature review is an opportunity to get a head start on the proposal and projects What is a Decision

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Strictly Proper Decision Markets

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A reminder about Problem set 2

  • Due in 8 days
  • Project proposals are due less than a week after
  • Literature review is an opportunity to get a head

start on the proposal and projects

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What is a Decision Market?

  • It’s a lot like a prediction market
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Discuss: Why do we speculate?

  • What are we running prediction markets for?
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History: Hanson writes an article

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Hanson’s decision markets

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Hanson’s decision markets

Quantitative Easing Helicopter Money No stimulus Adopting NDGP Possible Policies

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Hanson’s decision markets

Effect on GDP Quantitative Easing Helicopter Money No stimulus Adopting NDGP Possible Policies

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Hanson’s decision markets

Effect on GDP Quantitative Easing Helicopter Money No stimulus Adopting NDGP Possible Policies

?

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Hanson’s decision markets

Effect on GDP Quantitative Easing Helicopter Money No stimulus Adopting NDGP Possible Policies

?

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Hanson’s decision markets

Effect on GDP Quantitative Easing Helicopter Money No stimulus Adopting NDGP Possible Policies +.3% +.9%

  • .8%

+1.7%

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Hanson’s decision markets

Effect on GDP Quantitative Easing Helicopter Money No stimulus Adopting NDGP Possible Policies +.3% +.9%

  • .8%

+1.7%

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Hanson’s decision markets

Effect on GDP Quantitative Easing Helicopter Money No stimulus Adopting NDGP Possible Policies +.3% (?) +.9%(+1.5%)

  • .8% (?)

+1.7% (+1.1%)

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Philosophy: Markets with agency

Art’s vocation is to unveil the truth in the form of sensuous artistic configuration, to set forth the reconciled opposition just mentioned [the common world of earthly temporality, and a realm of thought and freedom], and so to have its end and aim in itself, in this very setting forth and unveiling. Hegel

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Philosophy: Markets with agency

If Hegel had written the whole of his logic and then said, in the preface or some other place, that it was merely an experiment in thought in which he had even begged the question in many places, then he would certainly have been the greatest thinker who had ever lived. As it is, he is merely comic. Kierkegaard

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Philosophy: Markets with agency

You love the accidental. A smile from a pretty girl in an interesting situation, a stolen glance, that is what you are hunting for, that is a motif for your aimless fantasy. You who always pride yourself on being an

  • bservateur must, in return, put up with

becoming an object of observation. Kierkegaard

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Philosophy: Markets with agency

And thus the native hue of resolution Is sicklied o'er with the pale cast of thought; And enterprises of great pith and moment, With this regard, their currents turn awry, And lose the name of action. Hamlet

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Markets where actions matter

  • Othman and Sandholm

▫ Single expert decision making

  • Chen and Kash

▫ Single expert decision making (generally)

  • Shi, Conitzer, Guo

▫ Principal-aligned scoring rules

  • Boutilier

▫ Self-interested experts

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Modeling Decision Markets

  • A decision maker considers
  • A set of possible actions, A

▫ E.g. up, down, invest in project A, hire person B, implement policy X, travel to Istanbul, etc.

  • A set of outcomes of interest, O

▫ Will we see a profit? Will public welfare increase? Will I eat some kebab?

  • And wants to learn the mapping from actions (A)

to outcomes (O) to make an informed decision

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Modeling Decision Markets

Step 1: Elicit action-outcome matrices

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Discuss: What are other examples?

  • And what drawbacks / possibilities are there for

each one?

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Modeling Decision Markets

Step 2: Create a decision policy

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Modeling Decision Markets

Step 2: Create a decision policy

Review market’s closing prediction

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Modeling Decision Markets

Step 2: Create a decision policy

Review market’s closing prediction Create probability distribution

  • ver the actions

80% 20% decision rule d

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Modeling Decision Markets

Step 3: Pick an action

80% 20%

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Modeling Decision Markets

Step 4: Observe the outcome

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Modeling Decision Markets

Step 5: Score experts

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Modeling Decision Markets

Step 5: Score experts

Actions (Springfield) Outcomes (Profit) Decision policy (.8, .2) Action-Outcome matrix

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Modeling Decision Markets

decision scoring rule scoring rule

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Discuss: why is strict properness important?

  • Because it totally is.
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Strict Properness for an expert

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Strict Properness for an expert

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Strict Properness for an expert

expected score

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Strict Properness for an expert

expected score

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Strict Properness for an expert

expected score how likely action a is to be taken given your report p (remember, only one expert so first report is the last report)

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Strict Properness for an expert

expected score how likely action a is to be taken given your report p (remember, only one expert so first report is the last report)

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Strict Properness for an expert

expected score how likely action a is to be taken given your report p (remember, only one expert so first report is the last report) your belief in the likelihood of

  • utcome o given action a is taken
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Strict Properness for an expert

expected score how likely action a is to be taken given your report p (remember, only one expert so first report is the last report) your belief in the likelihood of

  • utcome o given action a is taken
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Strict Properness for an expert

expected score how likely action a is to be taken given your report p (remember, only one expert so first report is the last report) your belief in the likelihood of

  • utcome o given action a is taken

score for your prediction given this action and outcome

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Strict Properness for an expert

The unique score maximizing prediction is always your true beliefs.

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Strict Properness for a market

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Discuss: why are markets different?

  • How many people are in a market? Not one

but…

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Strict Properness for a market

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Strict Properness for a market

decision policy now arbitrary

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Strict Properness for a market

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Strict Properness for a market

expected score

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Strict Properness for a market

expected score

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Strict Properness for a market

expected score in a prediction market this term is constant in a decision market it depends on d, the decision policy, which depends

  • n…
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Strictly Proper Pair

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Strictly Proper Pair

strict properness for an expert makes prior prediction constant

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Strictly Proper Pair

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Strict Properness Summary

  • Different constraints for a single expert and

many experts in a market

  • A strictly proper pair is strictly proper for both
  • These describe all of strictly proper for a market

pairs (minus some uninteresting basically the same set)

  • But not quite all of strict properness for an

expert

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Randomly taking any action is necessary

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Randomly taking any action is necessary

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Randomly taking any action is sufficient

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Randomly taking any action is sufficient

take a strictly proper scoring rule

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Randomly taking any action is sufficient

  • 1. take a strictly proper scoring rule
  • 2. divide by the inverse likelihood

the action is taken

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Randomly taking any action is sufficient

  • 1. take a strictly proper scoring rule
  • 2. divide by the inverse likelihood

the action is taken

  • 3. gives the same

expected value as many strictly proper prediction markets

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Example

80% 20%

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Example

(2/3 log 2/3 + 1/3 log 1/3) + (2/5 log 2/5 + 3/5 log 3/5) expected score using log scoring rule for two prediction markets

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Example

80% 20%

.8(2/3 log 2/3 + 1/3 log 1/3) + .2(2/5 log 2/5 + 3/5 log 3/5) expected score using log scoring rule

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Example

80% 20%

.8/.8(2/3 log 2/3 + 1/3 log 1/3) + .2/.2(2/5 log 2/5 + 3/5 log 3/5) expected score using (unbiased) log scoring rule

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Characterization

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Discuss: where does this leave us?

  • Are these markets practical/credible?
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Where the first prediction is also the last

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Hypothetical

  • I am a firm and I want to open a store in a city

that maximizes my profit.

  • I will open a store in whatever city you say.
  • I will pay you 1% of my eventual profit.
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Hypothetical

  • I am a firm and I want to open a store in a city

that maximizes my profit.

  • I will open a store in whatever city you say.
  • I will pay you 1% of my eventual profit.

Right-action rule (RAR)

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Research is fun (aside)

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Research is fun (aside) (part 2)

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Preferences

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Preferences

Previously we didn’t have to talk about preferences, but it turns out

  • nly some preferences have right-action rules!
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Preferences

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Preferences

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Preferences

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Preferences

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Discuss: single expert v. market

  • Sometimes one or the other?
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Discuss: where do we go from here?

  • the undiscovere'd country (?)
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Conclusion

  • Decision markets are part of an emerging

interest in “markets that do things”

  • This started as a 286r project

▫ Think big about your project!